Conditions of matrices in discrete tension spline approximations of DMBVP |
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Authors: | Mladen Rogina Sanja Singer |
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Institution: | (1) Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia;(2) Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia |
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Abstract: | Some splines can be defined as solutions of differential multi-point boundary value problems (DMBVP). In the numerical treatment
of DMBVP, the differential operator is discretized by finite differences. We consider one dimensional discrete hyperbolic
tension spline introduced in (Costantini et al. in Adv Comput Math 11:331–354, 1999), and the associated specially structured
pentadiagonal linear system. Error in direct methods for the solution of this linear system depends on condition numbers of
corresponding matrices. If the chosen mesh is uniform, the system matrix is symmetric and positive definite, and it is easy
to compute both, lower and upper bound, for its condition. In the more interesting non-uniform case, matrix is not symmetric,
but in some circumstances we can nevertheless find an upper bound on its condition number.
This research was supported by Grant 0037114, by the Ministry of Science, Education and Sports of the Republic of Croatia. |
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Keywords: | Discrete differential multi-point boundary value problem Uniform and non-uniform cases Bounds for condition of the associated linear system |
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